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e = 100 v.

fPEAH) k/) 1000 C.P.S.

=4=:C= IJUF

, INTEGRATOR OUTPUT (Cc)

I DIFFERENTIATOR OUTPUT (Cr)

OUTPUT WAVEFORM OF GENERATOR

- -- r 1Ц

/ OUTPUT OF DIFF-jrT EREgTIATOR(eRi

OUTPUT OF INTEGRATOR (ec)

-----90

Figure 31 RC DIFFERENTIATOR AND INTEGRATOR ACTION ON A SAWTOOTH WAVE

the capacitor conforms to the input voltage. Thus, the differentiator output becomes of particular importance in very short RC circuits. Differentiator outputs for various types of input waves are shown in figure 32.

Square Wave Test The application of a square for Audio Equipment wave input signal to audio equipment, and the observation of the reproduced output signal on an oscilloscope will provide a quick and accurate check of the overall operation of audio equipment. Low-frequency and high-frequency response, as well as transient response can be examined easily. If the amplifier is deficient in low-frequency response, the flat top of the square wave will be canted, as in figure 33. If the high-frequency response is inferior, the rise time of the output wave will be retarded (figure 34). An amplifier with a limited high-and low- frequency response will turn the square wave into the approximation of a sawtooth wave (figure (35)-

Transformers

When two coils are placed in such inductive relation to each other that the lines of force from one cut across the turns of the other inducing a current, the combination can be called a transformer. The name is derived from the fact that energy is transformed from one winding to another. The inductance in wiiich

Figure 32

Differentiator outputs of short r-e circuits for various Input voltage waveshapes. The output voltage Is proportional to the rate of change of the Input voltage.

the original flux is produced is called the primary; the inductance wiiich receives the induced current is called the secondary. In a radio receiver power transformer, for example, the coil through which the 110-volt a.c. passes is the primary, and the coil from which a higher or lower voltage than the a-c line potential is obtained is the secondary.

Transformers can have either air or magnetic cores, depending upon the frequencies at wiich they are to be operated. The reader should thoroughly impress upon his mind the fact that current can be transferred from one circuit to another only if the primary current is changing or alternating. From this it can be seen that a power transformer cannot possibly function as such when the primary is supplied with non-pulsating d.c.

A power transformer usually has a magnetic core which consists of laminations of iron, built up into a square or rectangular form, with a center opening or window. The secondary windings may be several in number, each perhaps delivering a different voltage. The secondary voltages will be proportional to the turns ratio and the primary voltage.

®

®

Figure 33

Amplifier deficient in low frequency reiponia will distort sqoare wave applied to fhe input circuit, as

shown. A iOCyela square wave may be used.

A: Drop in gain at low frequencies

Br Leading phase shift at low frequencies

C: Lagging phase shift at low frequencies

D: Accentuated law frequency gain

Types of Transformers are used in alter-Tronsformers nating-current circuits to transfer power at one voltage and impedance to anottier circuit at another voltage and impedance. There are three main classifications of transformers: those made for use in power-frequency circuits, those made for audio-frequency applications, and those made for radio frequencies.

The Tronsformotlon Rotio

In a perfect transformer all the magnetic flux lines produced by the primary winding link every turn of the secondary winding. For such a transformer, the ratio of the primary and secondary voltages is exactly the same as the ratio of the number of turns in the two windings:

Np Ep

where Np = number of turns in the primary winding

Ns = number of turns in the secondary winding

Ep = voltage across the primary winding

Eg = voltage across the secondary winding

In practice, the transformation ratio of a transformer is somewhat less than the turns ratio, since unity coupling does not exist between the primary and secondary windings.

Ampere Turns (N1) The current that flows in the secondary winding as a result of the induced voltage must produce a flux which exactly equals the primary flux. The magnetizing force of a coil is expressed as the product of the number of turns in the coil times the current flowing in it:

Is ip

Np X Ip = Ns X Is , or

where Ip = primary current

Is = secondary current

It can be seen from this expression that when the voltage is stepped up, the current is stepped down, and vice-versa.

Leakage Reactance Since unity coupling does not exist in a practical

Figure 34

Output waveshape af amplifier having deficiency In high-frequency response. Tested with lO-fce. square wave.

Figure 35

Output waveshape of amplifier having limited low-frequency and high-frequency response. Tested with 1-kc, square wave.

HANDBOOK

Electric Filters

о о

о о

 STEP-UP Zl ► JSTEP-DOWN INPUT 1 о оо Т оутрит 1 voiта&е О

Figure 36

IMPEDANCE-MATCHING TRANSFORMER

The reflected Impedartee 2p varies directly In proportion to the aeconaary

hod 2,

directly In proportion to the square of the prlmary-to-secondary turns ratio.

transformer, part of the flux passing from the primary circuit to the secondary circuit follows a magnetic circuit acted upon by the primary only. The same is true of the secondary flux. These leakage fluxes cause leakage reactance in the transformer, and tend to cause the traitsformer to have poor voltage regulation. To reduce such leakage reactance, the primary and secondary windings should be in close proximity to each other. The more expensive transformers have interleaved windings to reduce inherent leakage reactance.

Impedance Transformation

In the ideal transformer, the impedance of the secondary load is reflected back into the primary winding in the following relationship:

Zp = NZs , or N = VZp/Zs

where Zp = reflected primary impedance N = turns ratio of transformer Zs = impedance of secondary load

Thus any specific load connected to the secondary terminals of the transformer will be transformed to a different specific value appearing across rhe primary terminals of the transformer. By the proper choice of turns ratio, any reasonable value of secondary load impedance may be reflected into the primary winding of the transformer to produce the desired transformer primary impedance. The phase angle of the primary reflected impedance will be the same as the phase angle of the load impedance. A capacitive secondary load will be presented to the transformer source as a capacity, a resistive load will present a resistive reflection to the primary source. Thus the primary source sees a transformer load entirely dependent upon the secondary load impedance and the turns ratio of the transformer (figure 36).

The Auto The type of transformer in figure Transformer 37, when wound with heavy wire over an iron core, is a common device in primary power circuits for the purpose of increasing or decreasing the line volt-

Figure 37 THE AUTO-TRANSFORMER

Schematic diagram of on auto-transformer showing the method of connecting It to the line and to the load. When only a small amount of step up or step down Is required, the auto-transformer may be much smaller physically than would be a transformer with a separate secondary winding. Continuously variable auto-transfermers (Varlac and Powerslat) are widely used commercially.

age. In effect, it is merely a continuous winding with taps taken at various points along the winding, the input voltage being applied to the bottom and also to one tap on the winding. If the output is taken from this same tap, the voltage ratio will be 1-to-l; i.e., the input voltage will be the same as the output voltage. On the other hand, if the output tap is moved down toward the common terminal, there will be a step-down in the turns ratio with a consequent step-down in voltage. The initial setting of the middle input tap is chosen so that the number of turns will have sufficient reactance to keep the no-load primary current at a reasonably low value.

Electric Filters

There are many applications where it is desirable to pass a d-c component without passing a superimposed a-c component, or to

ELEMENTARY FILTER SECTIONS

L-3ECTI0Nt T-wetwohk

T T.

/±lneiwqrk

half-3ECTlON3

-K£№i--[II

T I T

¥i¥ 1

Figure 38

Compfex filters may be made up from these basic filter sections.

LOW-PASS SHUNT-DERIVED FILTER 0)

(series-arm resonated)

HIGH-PASS SERIES-DFRIVED FILTER

(SJHUNT-AHM RESONATED) Cl

<ZLZ

о о о

i It

2Lz Сг

r2 A:

FREQUENCY R= LOAD RESISTANCE Ll = M Ln Ci = xC.

c2= M ck

Гг= CUT-OFF FREQUENCY, Лс= FREQUENCY OF

HIGH ATTENUATION

Lk =

4-Л-/=

/ l = CUT-OFF FREQUENCY. iSc = FREQUENCY OF

HIGH ATTENUATION

Figure 39

TYPICAL LOW-PASS AND HIGH-PASS FILTERS, ILLUSTRATING SHUNT AND SERIES

DERIVATIONS

pass all frequencies above or below a certsiin frequency wiiile rejecting or attenuating all others, or to pass only a certain band or bands of frequencies while attenuating all others.

All of these things can be done by suitable combinations of inductance, capacitance and resistance. However, as whole books have been devoted to nothing but electric filters, it can be appreciated that it is possible only to touch upon them superficially in a general coverage book.

Filter Operation A filter acts by virtue of its property of offering very high impedance to the undesired frequencies, while offering but little impedance to the desired frequencies. This will also apply to d.c. with a superimposed a-c component, as d.c. can be considered as an alternating current of zero frequency so far as filter discussion goes.

Basic Filters Filters are divided into four classes, descriptive of the frequency bands which they are designed to transmit: high pass, low pass, band pass and band elimination. Each of these classes of filters is made up of elementary filter sections called L sections which consist of a series element {ZfJ and a parallel element (Zb) as

illustrated in figure 38. A finite number of L sections may be combined into basic filter sections, called T networks or pi networks, also shown in figure 38. Both the T and pi networks may be divided in two to form half-sections.

Filter Sections The most common filter section is one in which the two impedances Za and Zg are so related that their arithmetical product is a constant: Za x Zb = at all frequencies. This type of filter section is called a constant-K section.

A section having a shaфer cutoff frequency than a constant-K section, but less attenuation at frequencies far removed from cutoff is the tA-derived section, so called because the shunt or series element is resonated with a reactance of the opposite sign. If the complementary reactance is added to the series arm, the section is said to be shunt derived; if added to the shunt arm, series derived. Each impedance of the M-derived section is related to a corresponding impedance in the constant-K section by some factor which is a function of the constant m, M, in turn, is a function of the ratio between the cutoff frequency and the frequency of infinite attenuation, and will

HANDBOOK

Filter Design 65

-SECTION FILTER DESIGN

LOW PASS

R LOAD RESISTANCE /2 =CUT-OFF FREQUENCY

/ аэ= FREQUENCY OF VERY HIGH ATTENUATION

Lk =

TTfz R

CONSTANT К

iC2=f

Ll =Lk C2 = Ck

FREQUENCY

M = 0.6

f-)l2cll i I 1- 201

Ll = 0.6 Lk.= M Lk

- 1-M

Ci = 0.267 Ck = Сг = o.e Ck= M Ci

4тг

FREQUENCY

TERMINATING HALF-SECTIONS

>SAME VALUES AS M = 0.6

> SAME CURVE AS M = 0.6

71 = CUT-OFF FREQUENCY

/co=FREQUENCY OF VERY HIGH ATTENUATION

Lk =

HIGH PASS

о

-Z--о

Ci = Ck L2 = Lk

iHi-4ii

I о Г , . 2C< о I f I о) 2Ci

2L2a i u I 32L2

Ck =

3.7slk-XLK

0.6 M

4/7У1 R

I I

> SAME VALUES AS M = O.e

> SAME CURVE AS M = O.e

FREQUENCY

FREQUENCY

Figure 40

Through the use of the curves and equations which accompany the diagrams in the iliustratlon above it is possible to determine the correct values of inductance and capacitance for the usual types of pl-sectton

filters.

have some value between zero and one. As the value of m approaches zero, the sharpness of cutoff increases, but the less will be the attenuation at several times cutoff frequency, A value of 0.6 may be used for min most applications. The notch frequency is determined by the resonant frequency of the tuned filter element. The amount of attenuation obtained at the notch when a derived section is used is determined by the effective Q of the resonant arm (figure 39).

Filter Assembly Constant-K sections and derived sections may be cascaded to obtain the combined charactetistics of sharp cutoff and good remote frequency attenuation. Such a filter is known as a composite filter. The amount of attenuation will depend upon the number of filter sections used, and the shape of the transmission curve depends upon the type of filter sections used. All filters have some insertion loss. This attenuation is usually uniform to all frequen-

cies within the pass band. The insertion loss varies with the type of filter, the Q of the components and the type of termination employed.

Electric Filter Electric wave filters have long Design been used in some amateur sta-

tions in the audio channel to reduce the transmission of unwanted high frequencies and hence to reduce the bandwidth occupied by a radiophone signal. The effectiveness of a properly designed and properly used filter circuit in reducing QRM and sideband splatter should not be underestimated.

In recent years, high frequency filters have become commonplace in TVI reduction. High-pass type filters are placed before the input stage of television receivers to reject the fundamental signal of low frequency transmitters. Low-pass filters are used in the output circuits of low frequency transmitters to prevent harmonics of the transmitter from being radiated in the television channels.

Tlie chart of figure 40 gives design data and procedure on the pi-section type of filter. M-derived sections with an M of 0.6 will be found to be most satisfactory as the input section (or half-section) of the usual filter since the input impedance of such a section

is most constant over the pass band of the

filter section.

Simple filters may use either L, T, or n sections. Since the n section is i;he more commonly used type figure 40 gives design data and characteristics for this type of filter.

A PUSH-PULL 250-TH AMPLIFIER WITH TVI SHIELD REMOVED

Use ot harmonic Шеп in power feeds and агЧеппа circuit reduces radiation at TVI-producirtg harmonics of typical push-puil amplifier. Shielded enclosure completes harmonic reduction measures.

CHAPTER FOUR

Vacuum Tube Principles

In the previous chapters we have seen the manner in which an electric current flows through a metallic conductor as a result of an electron drift. This drift, wiiich takes place when there is a difference in potential between the ends of the metallic conductor, is in addition to the normal random electron motion between the molecules of the conductor.

The electron may be considered as a minute negatively charged pauticle, having a mass of 9 X 10- gram, and a charge of 1.59 X 10~ coulomb. Electrons are always identical, regardless of the source from which they are obtained.

An electric current can be caused to flow through other media than a metallic conductor. One such medium is an ionized solution, such as the sulfuric acid electrolyte in a storage battery. This type of current flow is called electrolytic conduction. Further, it was shown at about the turn of the century that an electric current can be carried by a stream of free electrons in an evacuated chamber. The flow of a current in such a manner is said to take place by electronic conduction. The study of electron tubes (also called vacuum tubes, or valves) is actually the study of the control and use of electronic currents within an evacuated or partially evacuated chamber.

Since the current flow in an electron tube takes place in an evacuated chamber, there must be located within the enclosure both a source of electrons and a collector for the electrons which have been emitted. The electron source is called the cathode, and the electron collector is usually called the anode. Some external source of energy must be applied to the cathode in order to impart sufficient velocity to the electrons within the cathode material to enable them to overcome the surface forces and thus escape into the surrounding medium. In the usual types of

electron tubes the cathode energy is applied in the form of heat; electron emission from a heated cathode is called thermionic emission. In another common type of electron tube, the photoelectric cell, energy in the form of light is applied to the cathode to cause photoelectric emission.

Thermionic Emission

Electron Emission of electrons from the Emission cathode of a thermionic electron tube takes place when the cathode of the tube is heated to a temperature sufficiently high that the free electrons in the emitter have sufficient velocity to overcome the restraining forces at the surface of the material. These surface forces vary greatly with different materials. Hence different types of cathodes must be raised to different temperatures to obtain adequate quantities of electron emission. The several types of emitters found in common types of transmitting and receiving tubes will be described in the following paragraphs.

Cathode Types The emitters or cathodes as used in present-day thermionic electron tubes may be classified into two groups: the direcdy-heated or filament typeaiid the indirectly-heated or heater-cathode type. Directly-heated emitters may be further subdivided into three important groups, all of which are commonly used in modern vacuum tubes. These classifications are: the pure-tungsten filament, the thoriated-tungsten filament, and the oxide-coated filament.

The Pure Tung- Pure tungsten wire was used sten Filoment as the filament in nearly all the earlier transmitting and

Figure 1 ELECTRON TUBE TYPES

The new Genera/ Electric ceramic triode (6BY4) is shown alongside a conventional miniature tube (626S) and an octal-based receiving tube (25L6). The ceramic tube is designed for rugged service and features extremely low lead inductance.

receiving tubes. However, the thermionic efficiency of tungsten wire as an emitter (the number of milliamperes emission per watt of filament heating power) is quite low, the filaments become fragile after use, their life is rather short, and they are susceptible to burnout at any time. Pure tungsten filaments must be run at bright white heat (about 2500° Kelvin). For these reasons, tungsten filaments have been replaced in all applications where another type of filament could be used. They are, however, still universally employed in large water-cooled tubes and in certain large, high-power air-cooled triodes where another filament type would be unsuitable. Tungsten filaments are the most satisfactory for high-power, high-voltage tubes where the emitter is subjected to positive ion bombardment caused by the residual gas content of the tubes. Tungsten is not adversely affected by such bombardment.

The Thoriated- In the course of experi-Tungsten Filament ments made upon tungsten emitters, it was found that filaments made from tungsten having a small amount of thoria (thorium oxide) as an impurity had much greater emission than those made from the pure metal. Subsequent development has resulted in the highly efficient car-burized thoriated-tungsten filament as used in virtually all medium-power transmitting tubes today.

Thoriated-tungsten emitters consist of a tungsten wire containing from 1% to 2% thoria. The activation process varies between different manufacturers of vacuum tubes, but it is essentially as follows: (1) the tube is evacuated; (2) the filament is burned for a short period at about 2800° Kelvin to clean the surface and reduce some of the thoria within the filament to metallic thorium; (3)

the filament is burned for a longer period at about 2100° Kelvin to form a layer of thorium on the surface of the tungsten; (4) the temperature is reduced to about 1600° Kelvin and some pure hydrocarbon gas is admitted to form a layer of tungsten carbide on the surface of the tungsten. This layer of tungsten carbide reduces the rate of thorium evaporation from the surface at the normal operating temperature of the filament and thus increases the operating life of the vacuum tube. Thorium evaporation from the surface is a natural consequence of the operation of the thoriated-tungsten filament. The carburized layer on the tungsten wire plays another role in acting as a reducing agent to produce new thorium from the thoria to replace that lost by evaporation. This new thorium continually diffuses to the surface during the normal operation of the filament. The last process, (5), in the activation of a thoriated tungsten filament consists of re-evacuating the envelope and then burning or ageing the new filament for a considerable period of time at the normal operating temperature of approximately 1900° K.

One thing to remember about any type of filament, particularly the thoriated type, is that the emitter deteriorates practically as fast when standing by (no plate current) as it does with any normal amount of emission load. Also, a thoriated filament may be either temporarily or permanently damaged by a heavy overload which may strip the surface layer of thorium from the filament.

Reactivating

Thoriated-Tungsten

Filaments

Thoriated-tungsten filaments (and otily thoriated-tungsten filaments) which have lost emission as a result of insufficient filament voltage, a severe temporary overload, a less severe extended overload, or even normal operation

HANDBOOK

Types of Emitters

Figure 2 V-H-F ond U-H-F TUBE TYPES

The fube to the left In this photograph Is a 955 acorn triode. The 6F4 acorn triode is very similar In appearance to the 955 jbuf has two leads brought out each for the grid and for the plate connection. The second tube is a 446A lighthouse triode. The 2C40, 2C43, and 2C44 are more recent examples of the same type tube and are essentially the same in external appearance. The third tube from the left Is a 2C39 oilcan lube. This tube type is essentially the Inverse of the lighthouse variety since the cathode and heater connections come out the small end and the plate Is the large finned radlotar on the large end. The use of the finned plate radiator malies the oilcan tube capable of approximateiy 10 times as much plate dissipation as the lighthouse type. The tube to the right Is the 4X1S0A beam tetrode. This tube, a comparatively recent release. Is capable of somewhat greater power output than any of the other tube types shown, and Is rated for full output at 500 Mc. and at reduced output at frequencies greater than

WOO Mc.

may quite frequently be reactivated to their original characteristics by a process similar to that of the original activation. However, only filaments which have not approached too close to the end of their useful life may be successfully reactivated.

The actual process of reactivation is relatively simple. The tube which has gone flat is placed in a socket to which only the two filament wires have been connected. The filament is then flashed for about 20 to 40 seconds at about 1/ times normal rated voltage. The filament will become extremely bright during this time and, if there is still some thoria left in the tungsten and if the tube did not originally fail as a result of an air leak, some of this thoria will be reduced to metallic thorium. The filament is then burned at 15 to 25 per cent overvoltage for from 30 minutes to 3 to 4 hours to bring this new thorium to the surface.

The tube should then be tested to see if it shows signs of renewed life. If it does, but is still weak, the burning process should be continued at about 10 to 15 per cent overvoltage for a few more hours. This should bring it back almost to normal. If the tube checks still very low after the first attempt at reactivation, the complete process can be repeated as a last effort.

The Oxide-Coated Filament

The most efficient of all modern filaments is the oxide-coated type which con-

sists of a mixture of barium and strontium oxides coated upon a nickel alloy wire or strip. This type of filament operates at a dull-red to orange-red temperature (1050 to 1170° K) at which temperature it will emit large quantities of electrons. The oxide-coated filament is somewhat more efficient than the thoriated-tungsten type in small sizes and it is considerably less expensive to manufacture. For this reason all receiving tubes and quite a number of the low-powered transmitting tubes use the oxide-coated filament. Another advantage of the oxide-coated emitter is its extremely long life - the average tube can be expected to run from 3000 to 5000 hours, and when loaded very lightly, tubes of this type have been known to give 50,000 hours of life before their characteristics changed to any great extent.

Oxide filaments are unsatisfactory for use at high continuous plate voltages because: (1) their activity is seriously impaired by the high temperature necessary to de-gas the high-voltage tubes and, (2) the positive ion bombardment which takes place even in the best evacuated high-voltage tube causes destruction of the oxide layer on the surface of the filament.

Oxide-coated emitters have been found capable of emitting an enormously large current pulse with a high applied voltage for a very short period of time without damage. This characteristic has proved to be of great value

Figure 3

CUT-AWAY DRAWING OF A 6C4 TRIODE

in radar work. For example, the relatively small cathode in a microwave magnetron may be called upon to deliver 25 to 50 amperes at an applied voltage of perhaps 25,000 volts for a period in the order of one microsecond. After this large current pulse has been passed, plate voltage normally will be removed for 1000 microseconds or more so that the cathode surface may be restored in time for the next pulse of current. If the cathode were to be subjected to a continuous current drain of this magnitude, it would be destroyed in an exceedingly short period of time.

The activation of oxide-coated filaments also varies with tube manufacturers but consists essentially in heating the wire which has been coated with a mixture of barium and strontium carbonates to a temperature of about 1500° Kelvin for a time and then applying a potential of 100 to 200 volts through a protective resistor to limit the emission current. This process reduces the carbonates to oxides thermally, cleans the filament surface of foreign materials, and activates the cathode surface.

Reactivation of oxide-coated filaments is not possible since there is always more than sufficient reduction of the oxides and diffusion of the metals to the surface of the filament to meet the emission needs of the cathode.

The Heater The heater type cathode was de-Cathode veloped as a result of the requirement for a type of emitter which could be operated from alternating current and yet would not introduce a-c ripple modulation even when used in low-level stages. It consists essentially of a small nickel-alloy cylinder with a coating of strontium and barium oxides on its surface similar to the coaling used on the oxide-coated filament. Inside the cylinder is an insulated heater element consisting usually of a double spiral of tungsten wire. The heater may operate on any volt-

age from 2 to 117 volts, although 6.3 is the

most common value. The heater is operated at quite a high temperature so that the cathode itself usually may be brought to operating temperature in a matter of 15 to 30 seconds. Heat-coupling between the heater and the cathode is mainly by radiation, although there is some thermal conduction through the insulating coating on the heater wire, as this coating is also in contact with the cathode thimble.

Indirectly heated cathodes are employed in all a-c operated tubes which are designed to operate at a low level either for r-f or a-f use. However, some receiver power tubes use heater cathodes (6L6, 6V6, 6F6, and 6K6-GT) as do some of the low-power transmitter tubes (802,807, 815, 3E29, 2E26, 5763, etc.). Heater cathodes are employed almost exclusively when a number of tubes are to be operated in series as in an a.c.-d.c. receiver. A heater cathode is often called a uni-potential cathode because there is no voltage drop along its length as there is in the directly-heated or filament cathode.

The Bombardment A special bombardment cath-Cathode ode is employed in many of

the new high powered television transmitting klystrons (Eimac 3K 20,000 LA). The cathode takes the form of a tantalum diode, heated to operating temperature by the bombardment of electrons from a directly heated filament. The cathode operates at a positive potential of 2000 volts with respect to the filament, and a d-c bombardment current of 0.66 amperes flows between filament and cathode. The filament is designed to operate under space-charge limited conditions. Cathode temperature is varied by changing the bombardment potential between the filament and the cathode.

The Emission The emission of electrons from Equation a heated cathode is quite sim-

ilar to the evaporation of molecules from the surface of a liquid. The molecules which leave the surface are those having sufficient kinetic (heat) energy to overcome the forces at the surface of the liquid. As the temperature of the liquid is raised, the average velocity of the molecules is increased, and a greater number of molecules will acquire sufficient energy to be evaporated. The evaporation of electrons from the surface of a thermionic emitter is similarly a function of average electron velocity, and hence is a function of the temperature of the emitter.

Electron emission per unit area of emitting surface is a function of the temperature T in degrees Kelvin, the work function of the emitting surface b (which is a measure of the

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